clara {cluster} | R Documentation

## Clustering Large Applications

### Description

Computes a `"clara"` object, a list representing a clustering of the data into `k` clusters.

### Usage

    clara(x, k, metric = "euclidean", stand = FALSE, samples = 5,
          sampsize = 40 + 2 * k, trace = 0, keep.data = TRUE, keepdata,
          rngR = FALSE)

### Arguments

`x` | data matrix or data frame, each row corresponds to an observation, and each column corresponds to a variable. All variables must be numeric. Missing values (NAs) are allowed.
`k` | integer, the number of clusters. It is required that 0 < k < n where n is the number of observations (i.e., n = `nrow(x)`).
`metric` | character string specifying the metric to be used for calculating dissimilarities between observations. The currently available options are "euclidean" and "manhattan". Euclidean distances are root sum-of-squares of differences, and manhattan distances are the sum of absolute differences.
`stand` | logical, indicating if the measurements in `x` are standardized before calculating the dissimilarities. Measurements are standardized for each variable (column), by subtracting the variable's mean value and dividing by the variable's mean absolute deviation.
`samples` | integer, number of samples to be drawn from the dataset.
`sampsize` | integer, number of observations in each sample. `sampsize` should be higher than the number of clusters (`k`) and at most the number of observations (n = `nrow(x)`).
`trace` | integer indicating a trace level for diagnostic output during the algorithm.
`keep.data,keepdata` | logical indicating if the (scaled if `stand` is true) data should be kept in the result. (`keepdata` is equivalent to `keep.data` where the former is deprecated.) Setting this to `FALSE` saves memory (and hence time), but disables `clusplot()`ing of the result.
`rngR` | logical indicating if R's random number generator should be used instead of the primitive clara()-builtin one. If true, this also means that each call to `clara()` returns a different result – though only slightly different in good situations.

### Details

`clara` is fully described in chapter 3 of Kaufman and Rousseeuw (1990). Compared to other partitioning methods such as `pam`, it can deal with much larger datasets. Internally, this is achieved by considering sub-datasets of fixed size (`sampsize`) such that the time and storage requirements become linear in n rather than quadratic.

Each sub-dataset is partitioned into `k` clusters using the same algorithm as in `pam`.
Once `k` representative objects have been selected from the sub-dataset, each observation of the entire dataset is assigned to the nearest medoid.

The sum of the dissimilarities of the observations to their closest medoid is used as a measure of the quality of the clustering. The sub-dataset for which the sum is minimal, is retained. A further analysis is carried out on the final partition.

Each sub-dataset is forced to contain the medoids obtained from the best sub-dataset until then. Randomly drawn observations are added to this set until `sampsize` has been reached.

### Value

an object of class `"clara"` representing the clustering. See `clara.object` for details.

### Note

By default, the random sampling is implemented with a very simple scheme (with period 2^{16} = 65536) inside the Fortran code, independently of R's random number generation, and as a matter of fact, deterministically. Alternatively, we recommend

The storage requirement of `clara` computation (for small `k`) is about O(n * p) + O(j^2) where j = `sampsize`, and (n,p) = `dim(x)`. The CPU computing time (again neglecting small `k`) is about O(n * p * j^2 * N), where N = `samples`.

For ``small'' datasets, the function `pam` can be used directly. What can be considered small, is really a function of available computing power, both memory (RAM) and speed. Originally (1990), ``small'' meant less than 100 observations; later, the authors said ``small (say with fewer than 200 observations)''..

### Author(s)

Kaufman and Rousseuw, originally. All arguments from `trace` on, and most R documentation and all tests by Martin Maechler.

### See Also

`agnes` for background and references; `clara.object`, `pam`, `partition.object`, `plot.partition`.

### Examples

    ## generate 500 objects, divided into 2 clusters.
    x <- rbind(cbind(rnorm(200,0,8), rnorm(200,0,8)),
               cbind(rnorm(300,50,8), rnorm(300,50,8)))
    clarax <- clara(x, 2)
    clarax
    clarax$clusinfo
    plot(clarax)

    ## `xclara' is an artificial data set with 3 clusters of 1000 bivariate
    ## objects each.
    data(xclara)
    (clx3 <- clara(xclara, 3))
    ## Plot similar to Figure 5 in Struyf et al (1996)
    ## Don't run: plot(clx3, ask = TRUE)

    ## Try 100 times *different* random samples -- for reliability:
    nSim <- 100
    nCl <- 3 # = no.classes
    set.seed(421)# (reproducibility)
    cl <- matrix(NA,nrow(xclara), nSim)
    for(i in 1:nSim) cl[,i] <- clara(xclara, nCl, rngR = TRUE)$cluster
    tcl <- apply(cl,1, tabulate, nbins = nCl)
    ## those that are not always in same cluster (5 out of 3000 for this seed):
    (iDoubt <- which(apply(tcl,2, function(n) all(n < nSim))))
    if(length(iDoubt)) { # (not for all seeds)
      tabD <- tcl[,iDoubt, drop=FALSE]
      dimnames(tabD) <- list(cluster = paste(1:nCl), obs = format(iDoubt))
      t(tabD) # how many times in which clusters
    }

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